An upper bound on the average size of silhouettes

It is a widely observed phenomenon in computer graphics that the size of the silhouette of a polyhedron is much smaller than the size of the whole polyhedron. This paper provides, for the first time, theoretical evidence supporting this for a large class of objects, namely for polyhedra that approximate surfaces in some reasonable way; the surfaces may be non-convex and non-differentiable and they may have boundaries. We prove that such polyhedra have silhouettes of expected size O( √ n) where the average is taken over all points of view and n is the complexity of the polyhedron.

• Type: Conference
• Year: 2006
• Where: COMPGEOM
• Authors: Marc Glisse
• Keywords: COMPGEOM 2006, Polyhedron, Theoretical Evidence, first Time